The paper summarises recent developments pursued by the unsteady aerodynamics group at QMW. These include the development of computational fluid dynamics methods and validation of turbulence models for essentially unsteady flows with moving boundaries as well as investigation of various unsteady aerodynamic phenomena including dynamic stall, buffet, flutter and unsteady shock-wave diffraction. Overall, these studies have so far shown that simulations of unsteady aerodynamic flows which are strongly affected by turbulence, can provide a fair qualitative picture in most of the cases, but there are still many open issues regarding the quantitative agreement between experiments and simulations. Particular challenges and remaining open questions appear in the case of unsteady flows around pitching and oscillating aerofoils featuring dynamic stall. The various results indicate some strengths of the Godunov-type methods, implicit solvers, as well as linear, non-linear (eddy-viscosity-based) and Reynolds-stress models employed in this study, but they also reveal weaknesses associated in particular with modelling issues of high Reynolds number compressible flows.